75 research outputs found
Degenerate Whittaker functionals for real reductive groups
In this paper we establish a connection between the associated variety of a
representation and the existence of certain degenerate Whittaker functionals,
for both smooth and K-finite vectors, for all quasi-split real reductive
groups, thereby generalizing results of Kostant, Matumoto and others.Comment: 22 pages. v2: exposition improved, typos corrected. To appear in
Amer. Jour. of Mat
Intertwining operators between line bundles on Grassmannians
Let G=GL(n,F) where F is a local field of arbitrary characteristic, and let
be representations induced from characters of two maximal
parabolic subgroups . We explicitly determine the space
of intertwining operators and prove that it has dimension
at most 1 in all cases.Comment: 7 page
Invariant Functionals on the Speh representation
We study Sp(2n,R)-invariant functionals on the spaces of smooth vectors in
Speh representations of GL(2n,R).
For even n we give expressions for such invariant functionals using an
explicit realization of the space of smooth vectors in the Speh
representations. Furthermore, we show that the functional we construct is, up
to a constant, the unique functional on the Speh representation which is
invariant under the Siegel parabolic subgroup of Sp(2n,R). For odd n we show
that the Speh representations do not admit an invariant functional with respect
to the subgroup U(n) of Sp(2n,R) consisting of unitary matrices.
Our construction, combined with the argument in [GOSS12], gives a purely
local and explicit construction of Klyachko models for all unitary
representations of GL(2n,R).Comment: 14 pages. v4: minor corrections in Theorem 2.2, Lemma 2.9 and section
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